Continuum mechanics has been used for simulating continuous matter such as solids and fluids (i.e., liquids and gases). Differential equations are employed in solving problems in continuum mechanics. Many numerical procedures have been used. One of the most popular methods is finite element analysis (FEA), which is a computerized method widely used in industry to model and solve engineering problems relating to complex systems such as three-dimensional non-linear structural design and analysis. FEA derives its name from the manner in which the geometry of the object under consideration is specified. With the advent of the modern digital computer, FEA has been implemented as FEA software. Basically, the FEA software is provided with a grid-based model of the geometric description and the associated material properties at each point within the model. In this model, the geometry of the system under analysis is represented by solids, shells and beams of various sizes, which are called elements. The vertices of the elements are referred to as nodes. The model is comprised of a finite number of elements, which are assigned a material name to associate with material properties. The model thus represents the physical space occupied by the object under analysis along with its immediate surroundings. The FEA software then refers to a table in which the properties (e.g., stress-strain constitutive equation, Young's modulus, Poisson's ratio, thermo-conductivity) of each material type are tabulated. Additionally, the conditions at the boundary of the object (i.e., loadings, physical constraints, etc.) are specified. In this fashion a model of the object and its environment is created.
Once the model is defined, FEA software can perform a simulation of the physical behavior under the specified loading or initial conditions. FEA software is used extensively in the automotive industry to simulate front and side impacts of automobiles, occupant dummies interacting with airbags, and the forming of body parts from sheet metal. Such simulations provide valuable insight to engineers who are able to improve the safety of automobiles and to bring new models to the market more quickly. The simulation is generally performed in time domain meaning the FEA is computed at many solution cycles starting from an initial solution cycle, at each subsequent solution cycle, the simulation time is incremented by a time step referred to as ΔT.
Solid elements are typically used for modeling thick parts or solid bodies. In three dimensions, a solid element can be shaped like brick or hexahedron. The lowest order brick element has a node at each corner and is thus called the 8-node brick or hexahedral element. The compatible stress and strain fields have linear terms within the element domain. There are other types of solid elements such the 6-node pentahedral element.
One of the most challenging FEA tasks is to simulate an impact event involving structural fracture. As the modern computer improves, engineers not only wish to simulate the behavior in an impact event with structural failure or fracture, they also want to simulate debris resulting from the impact. However, the debris is not suitable with by solving a continuum mechanics problem using a FEA.
Another problem in FEA is the adaptivity. In order to get more accurate simulation, it is preferable to refine the FEM grid model around the region of interest (e.g., contact region in an impact event). However, the adaptivity is not very easy performed in the FEA.
Given the foregoing drawbacks, problems and limitations of the prior art, it would be desirable to have improved methods and systems to perform engineering analysis that can simulate an impact event with structural failure or fracture including the resulting debris.